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\begin{document}

\title{A Comparison of Approaches to Model Uncertainty in Time Intervals}

\begin{aug}
\author[1]{Christophe Billiet}
\author[2]{Jos\'{e} Enrique Pons}
\author[2]{Olga Pons Capote}
\author[1]{Guy de Tr\'{e}}
\affilation[1]{Department of Telecommunications and Information Processing, Ghent University, Belgium.
%\\ Sint-Pietersnieuwstraat 41, B-9000 Ghent, Belgium
}
\affilation[2]{Department of Computer Science and Artificial Intelligence, University of Granada, Spain.
%\\ C/Periodista Daniel Saucedo Aranda s/n E-18071 (Granada-Spain)
}
\end{aug}


\maketitle
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\begin{abstract}
Information systems model parts of reality by representing properties of real-world objects or concepts. As real objects or concepts often have temporal aspects, temporal notions such as time intervals are often represented. However, these may contain imperfections like uncertainties, complicating their representations. A very important purpose of information systems is to be able to query them to retrieve information, but representations of temporal notions containing uncertainties severely complicate querying. Thus, several soft computing techniques have been proposed to represent time intervals subject to uncertainties in a semantically sound way and to reason with them in a semantically sound and useful way. In the presented work, two frameworks designed for this are compared. It is found that, despite slight differences in the way these frameworks represent intervals, they provide the same results when reasoning about time intervals subject to uncertainty.
\end{abstract}

\begin{keywords}
temporal representation, temporal reasoning, possibility theory, information systems, information retrieval, ill-known intervals, uncertainty
\end{keywords}

\section{\label{sec:introduction}Introduction}
\input{introduction}

\section{\label{sec:general-preliminaries}General Preliminaries, Notations and Nomenclature}
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\section{\label{sec:ikc}The Ill-known Constraint Framework}
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\section{\label{sec:tm}The Triangular Model Framework}
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\section{\label{sec:proposal}Comparison of Both Frameworks}
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\section{\label{sec:conclusions}Conclusions}
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\vspace{-10pt}
\section*{Acknowledgements}
\vspace{-5pt}
Part of the research is supported by the grant BES-2009-013805 within the research project TIN2008-02066: \emph{Fuzzy Temporal Information treatment in relational DBMS}.

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